The Finn, who was given a pay-off to end his contract early, then spent two years in the World Rally Championship before returning to F1 with Lotus.
He has since been a race-winner and title contender, a performance that di Montezemolo believes emulates Lauda - who walked away from the sport in late-1979 but returned with McLaren in '82 and was champion for a third time two years later.
"Raikkonen's case is identical to Lauda's," di Montezemolo told Italian newspaper Gazzetta dello Sport.
"At some point, Niki too said 'enough' because he couldn't stand it anymore.
"I had talked about Kimi's twin brother because the driver racing for us wasn't the same one we had hired.
"The stop has done him well, he has made a great comeback, he has won and finished many races."
From the archive: why Raikkonen is walking away from F1
"I wanted a race driver who wouldn't make me regret Massa: here he is," di Montezemolo said.
"From Raikkonen I ask for victories, consistency, podiums. Alonso is the first in line in taking advantage from that.
"I'm happy he's back with us, Ferrari personnel were enthusiastic with the news because he had left good memories."
FERRARI 'NOT MASOCHISTS'
The president underlined that signing Raikkonen had not destabilised Alonso.
"We are not such masochists as to hire a race driver without informing Alonso," di Montezemolo said.
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"Fernando has always been informed of the decision on Raikkonen, also because the alternative of a youngster, in a season as complex as 2014, wouldn't give us certainties.
"Nowadays Raikkonen is the strongest, together with Alonso, [Sebastian] Vettel and [Lewis] Hamilton.
"Alonso is the first one satisfied with his arrival."
Translation by Michele Lostia